Problem AG01 innermost 4.20a

Tool Bounds

Execution Time	60.030514ms
Answer	TIMEOUT
Input	AG01 innermost 4.20a

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  g(s(0())) -> g(f(s(0())))
     , f(s(x)) -> f(x)
     , f(f(x)) -> f(x)}
  StartTerms: all
  Strategy: none

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool CDI

Execution Time	3.181819ms
Answer	YES(?,O(n^2))
Input	AG01 innermost 4.20a

stdout:

YES(?,O(n^2))
QUADRATIC upper bound on the derivational complexity

This TRS is terminating using the deltarestricted interpretation
0(delta) =  + 0 + 0*delta
g(delta, X0) =  + 0*X0 + 0 + 2*X0*delta + 0*delta
s(delta, X0) =  + 0*X0 + 3 + 1*X0*delta + 0*delta
f(delta, X0) =  + 0*X0 + 1 + 1*X0*delta + 0*delta
g_tau_1(delta) = delta/(0 + 2 * delta)
s_tau_1(delta) = delta/(0 + 1 * delta)
f_tau_1(delta) = delta/(0 + 1 * delta)

Time: 3.145609 seconds
Statistics:
Number of monomials: 297
Last formula building started for bound 3
Last SAT solving started for bound 3

Tool EDA

Execution Time	0.43698215ms
Answer	YES(?,O(n^2))
Input	AG01 innermost 4.20a

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  g(s(0())) -> g(f(s(0())))
     , f(s(x)) -> f(x)
     , f(f(x)) -> f(x)}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^2))

Proof:
  We have the following EDA-non-satisfying matrix interpretation:
  Interpretation Functions:
   f(x1) = [1 1] x1 + [2]
           [0 0]      [0]
   s(x1) = [1 1] x1 + [0]
           [0 0]      [3]
   0() = [0]
         [0]
   g(x1) = [1 3] x1 + [0]
           [0 0]      [1]

Hurray, we answered YES(?,O(n^2))

Tool IDA

Execution Time	0.6144719ms
Answer	YES(?,O(n^2))
Input	AG01 innermost 4.20a

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  g(s(0())) -> g(f(s(0())))
     , f(s(x)) -> f(x)
     , f(f(x)) -> f(x)}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^2))

Proof:
  We have the following EDA-non-satisfying and IDA(2)-non-satisfying matrix interpretation:
  Interpretation Functions:
   f(x1) = [1 1] x1 + [2]
           [0 0]      [0]
   s(x1) = [1 1] x1 + [0]
           [0 0]      [3]
   0() = [0]
         [0]
   g(x1) = [1 3] x1 + [0]
           [0 0]      [1]

Hurray, we answered YES(?,O(n^2))

Tool TRI

Execution Time	0.16492414ms
Answer	YES(?,O(n^1))
Input	AG01 innermost 4.20a

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  g(s(0())) -> g(f(s(0())))
     , f(s(x)) -> f(x)
     , f(f(x)) -> f(x)}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^1))

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   f(x1) = [1 1] x1 + [1]
           [0 0]      [0]
   s(x1) = [1 1] x1 + [0]
           [0 0]      [1]
   0() = [0]
         [1]
   g(x1) = [1 3] x1 + [0]
           [0 0]      [1]

Hurray, we answered YES(?,O(n^1))

Tool TRI2

Execution Time	0.14205122ms
Answer	YES(?,O(n^2))
Input	AG01 innermost 4.20a

stdout:

YES(?,O(n^2))

We consider the following Problem:

  Strict Trs:
    {  g(s(0())) -> g(f(s(0())))
     , f(s(x)) -> f(x)
     , f(f(x)) -> f(x)}
  StartTerms: all
  Strategy: none

Certificate: YES(?,O(n^2))

Proof:
  We have the following triangular matrix interpretation:
  Interpretation Functions:
   f(x1) = [1 0] x1 + [3]
           [0 0]      [1]
   s(x1) = [1 3] x1 + [1]
           [0 1]      [3]
   0() = [0]
         [2]
   g(x1) = [1 2] x1 + [0]
           [0 0]      [1]

Hurray, we answered YES(?,O(n^2))